Schrödinger's paradox

In 1935 the physicist Erwin Schrödinger published an article on "The Present situation in Quantum-Mechanics". As an aside, he formulated what is now called Schrödinger's paradox. [Schrödinger, 1935]. This paradox has since fascinated millions.
Physicists in quantum-mechanics work with a notion called uncertainty, which is governed by the Heisenberg uncertainty relation. When we measure the state of an atom, we measure its location, speed, energy, et cetera. Heisenberg states that we can never perform all these measurements with total certainty, there is always an uncertainty in the result.
Here, it is important to realize that an atom can decay, and that with the decay radio-active radiation is released. The moment of decay is uncertain, in the Heisenberg sense of the word. True, for a large number of atoms, we know the average half-life of the atom. But for a single atom it is impossible to predict the moment of decay. If one puts a single atom in a box, the only way to know whether it has decayed is to open the box and look inside.
On this uncertainty, Schrödinger writes: "One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. (This acid will kill the cat). If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. In quantum-mechanics one would express this by simultaneously having both a living and a dead cat" [Schrödinger, 1935, my italics].
Schrödinger goes on to remark that the importance of this example lies in "the (Heisenberg) uncertainty originally restricted to the atomic domain becomes transformed into uncertainty at the human domain, which can then be resolved by direct observation (by opening the door of the chamber and looking inside to see if the cat still lives)." [Schrödinger, 1935, my italics].
This thought-experiment has fascinated many, in particular the question: What is the state of the cat if I do not look inside the chamber, is the cat alive, dead, or both alive and dead at the same time?
Schrödinger answers this question as follows: "From this very hard dilemma the reigning doctrine rescues itself by having recourse to epistemology. We are told (Schrödinger does not tell us by whom) that no distinction is to be made between the state of a natural object and what I know about it, or perhaps better, what I can know about it if I go to some trouble. Actually - so they say - there is intrinsically only awareness, observation, measurement. If through them I have procured at a given moment the best knowledge of the state of the physical object that is possibly attainable in accord with Heisenberg's uncertainty relation, then I can turn aside as meaningless any further questioning about the "actual state",..." [Schrödinger, 1935, my italics]
I assume that by "turning aside as meaningless" Schrödinger consciously uses a positivist’s phrase. Schrödinger seems very much aware of the important philosophical consequences of his "turning aside as meaningless". He assures us that this philosophical principal "no sensible person can fail to esteem as the supreme protector of all Empiricism".
So, to Schrödinger his thought-experiment about the cat does not pose a paradox. To him, the correct definition of a "state" is "an observed state" and it would be inconsistent to speak of an unobserved state.

On the other hand, human reason appears unable to restrict itself to observed states. We can only think of a state in and of itself, irrespective of observation or not.
Schrödinger's paradox illustrates how human reason breaks down in understanding quantum-mechanics. This probably should come as no surprise, as human reason was, during evolution, never tested in that realm.